Aristotle believed that events are happening in the way they are happening because of some purpose – because of some "mandatory" final state that everything must converge to. Carroll admits that science was being built on "dysteleological physicalism" but he still defends the musings by "smart cookie" Aristotle by many pseudoarguments.

If you think about the word "purpose" and if you realize that this is a favorite religious theme in the context of "God's plans", you can't be too surprised that Aristotle became a darling of the medieval Catholic bigots who have hijacked the education system and introduced the system of mindless mass indoctrination by worthless, dogma-based pseudoknowledge. This indoctrination was known as "scholasticism". This attitude was among the main reasons why the Dark Ages were so dark; why scientific, technological, and social progress has virtually stopped for many long centuries.

Scholasticism was reconciling many of the pernicious tendencies that the education and scholarship has ever suffered from. It was defending dogmas but never tried to question them or consider new alternatives; it was constantly hyping or worshiping the authorities and fake authorities; it was making proponents of existing philosophies "debate" but the debate has always been meaningless because no one was ever supposed to eliminate the wrong philosophies (in this sense, it was as defective as much of the politically correct education today). And scholasticism loved to impress itself and the students with lots of unnecessarily complicated words and jargon whose usefulness has just never matched the efforts needed to learn all the pompous terminology.

If you look at every single feature of their methods and their union, you must agree that the system was designed so that nothing can ever get improved in the intellectual landscape. Their values were really opposite to the values of science. Science always allows one to challenge the dogmas, find and test alternatives, ignore the authorities, change the initial balance of influence according to the evidence, eliminate falsified hypotheses, and achieve a lot with a minimum vocabulary.

Physics would soon figure out that the future is evolving from the past and it's never working in the opposite direction (yes, it's a point that Carroll is de facto denying in all his writing about the arrow of time). That's how Newton and others would look at the problem. However, people also found the principle of least action that says\[

\delta S = 0

\] that the action (the integral of the Lagrangian over time) is minimized (or extremized) on the trajectory or history that is actually allowed by Nature, among all conceivable trajectories or histories with the same initial conditions in the past and the same final conditions in the future. Because we're sort of "forced" to talk about "what things could look like in the future", the law looks teleological. However, a mathematical derivation of Euler-Lagrange equations implies that for a Lagrangian that is local in time, the principle of least action is equivalent to differential equations so it is really dysteleological in every physical sense. The teleology behind \(\delta S = 0\) is just an illusion.

The principle of least action turned out to be sufficient to formulate all fundamental laws in classical physics. In quantum physics, it is replaced by Feynman's path integral. All histories of the quantum system contribute to the probability amplitudes for some evolution by the term \(\exp(iS/\hbar)\). These complex numbers with the same absolute value (one) tend to average almost accurately because \(S\) i.e. the direction in the complex plane is "random". Only trajectories near those that solve \(\delta S=0\) have a "slowly changing \(S\)" so that they constructively interfere and cancellation goes away; the classically allowed trajectory becomes the most important one in quantum physics (in the classical limit), too. That's how the principle of least action (and classical physics) emerges from Feynman's path integral (and quantum mechanics). Also, quantum mechanics becomes "more straightforward" than classical physics. In classical physics, the answer to physical questions is determined from a solution to equations \(\delta S = 0\) – so the right history is defined "implicitly" (by equations it has to obey). In quantum physics, we may write the answers to everything "explicitly" (we may write all probability amplitudes as a path integral).

Feynman's path integral could also look "teleological" because we may sum over histories of the physical system that include the evolution in the future. However, the result of this integration is just a prediction of (probabilities of) observations in the final state. It means that in practice, we never want to consider a "more distant future" than the "future up to the measurements we care about". Again, Feynman's potentially teleological laws are equivalent to Heisenberg's or Schrödinger's equations of motion that dictate the evolution of the physical system from one moment to the next. Whether or not "teleology" may be added as an extra condition is being debated in the context of the "black hole final state" by Maldacena and Horowitz. In recent years, I have grown increasingly (but not quite) certain than the answer is "No". The locality in the deep interior of the black hole just shouldn't be taken too seriously, it's just being marginally reconstructed from the event horizon, and at some place (the singularity), the extrapolation just breaks down and becomes impossible. I tend to think that the singularity is reached in a generic state.

Feynman's path integrals and quantum mechanics in general force us to do another "semiteleological" procedure, however: they force us to deny the existence of "intermediate facts" that are not measured. So if particle is just going through a double slit, you can't ask which one it is (even though you would get an answer if you actually decided to measure the "which slit" bit; but that would change the results of the experiment). You may describe the properties of the particle around the double slit using a wave function. But the wave function isn't a "reality". In some sense, it's purpose is just a teleological one – we use it because we may predict the results in the future but it is in no way a "reality at the present". But note that I am not saying that the actual laws are teleological; I am just saying that the interpretation of a mathematical object in the theory is "teleological" in a related sense which is not equivalent, however. ("Teleological" added in front of a "theory" cannot be quite the same thing as the adjective added in front of a completely inequivalent word "wave function".)

But let me return to more elementary points – Carroll's defense of teleology. He writes:

However. Aristotle was a smart cookie, and dismissing him as an outdated relic is always a bad idea.

Well, I would say that Aristotle was an insanely overrated and quickly outdated relic and considering him as a smart cookie has always been a bad idea – one that "helped" Europe to avoid progress for 500-1,000 years. He liked to write about everything but none of the newly contributed wisdoms and would-be scientific insights he guessed was really right.

Take his "golden mean" in philosophy (not the mathematical ratio). The average between extremes is the best, Aristotle claimed. Well, it's surely not. It's only best for the promotion of mediocrity and stagnation; no wonder that Aristotle would be a hero for many mediocre people. Extremes may have some undesirable features but these vices are in no way "unavoidable" and there's no reason why the average elements according to the current distributions should be better than the extreme ones, and so on. The "golden mean" has to be located according to some distribution and Aristotle obviously had to take the current one, thus prohibiting any kind of progress (which always includes some drift away from the current average). For this reason, "golden mean" has always been just a rationalization of stagnation, an ideology allowing people to be satisfied with themselves.

He would coin "term logic". It may be viewed as a less comprehensible ancestor of the modern predicate logic. Aristotle just made a big deal of it but I don't believe for a second that the previous mathematicians and philosophers didn't understand the "beef of logic". They would know how to deduce \(B\) from \(A\) and \(A\Rightarrow B\) even though they didn't know words like "syllogism" (introduced by Aristotle). Moreover, he wouldn't really describe any symbols or truly rigorous methods to deal with the logical operations. So his rules were always "somewhere in between the rules of maths and the rules of grammar". This is a dangerous combination because the human language is much more informal than logical or mathematical reasoning. By having claimed that those are pretty much the same thing, the Aristotelian viewpoint on logic made it hard to separate careful, controllable thinking from a vague, linguistic thinking. And that's too bad.

Aristotle would love to define new, pretty much useless words – words that have no reason to be used often if you talk about the issues rationally. For example, the word "hexis" was some hybrid of "stability", "disposition", "gene", "virtue", and so on. He would write down definitions and people were supposed to be impressed with such definitions, especially because they were mixing many words together. But this mixing is really a vice, it is a wrong direction for the evolution of the language. As this eclectic mixing of different words exemplifies, his thinking was often opposite to the analytic thought that tries to separate the building blocks and isolate the actual reasons; and believe me that saying that "synthetic" is just a euphemism for the opposite of "analytic". Of course, it's true for most philosophers that they really dislike to think analytically.

Or take "hylomorphism". Being is a union of matter and form. Great. Did he find anything except of another useless word? Do you really believe that the thinkers before Aristotle didn't know that both matter and the form was important for being? Or did they just find it sensible not to hype these quasi-tautologies much? Aristotle would identify the "form" with "soul" and he would say many protoscientific things about the life.

Most of his comments about biology would be vague, semi-wrong memes like "every organism has to be able to nourish and reproduce because we see that plants can do it" and plants were the most primitive organisms for him (well, that's also wrong, but let's not protest much). But at random points, he would supplement his theories with untested and indefensible far-reaching gems like "spontaneous generation": organisms are created directly from some inorganic matter, from dust and mud, and from dead bodies, as long as those look similar to the organism we want to create. Now, this is really stupid. He could have tested this bold proposal. Burn some wood and mix the ashes with pure water and see whether butterflies emerge from the mix. They wouldn't. He didn't care. He just completely failed to distinguish guesses from tested propositions, and so did tons of followers in the following 1,500 years (well, 2,000 years) or so. Remarkably, he also couldn't count the women's teeth – a pretty bad for an ancient defender of "empirical" approaches. Women would be the "passive element" while the masculine elements pumps activity to everything. It may be somewhat correlated with some reality but to turn it into a dogma is silly.

Aristotelian "physics" was a sequence of fundamental misconceptions from the beginning to the end. The vacuum couldn't exist, everything was made of 5 elements, aether was one of them, without a force, bodies would stay at rest, \(F=mv\) instead of \(F=ma\), atoms couldn't exist, celestial bodies were carried by crystal spheres, the sum of angles in a triangle is always three (OK, I added this one, so that he gets at least one thing "right"), celestial materials had to fundamentally differ from the terrestrial ones, and so on, and so on. Those are similar guesses as many countryside philosophers would offer today (or earlier). His comments were never evaluated according to their validity, just according to his (rationally indefensible) authority. Muslims would call him "the first teacher" and the love had to be deep because the Muslims generally love to brainwash and be brainwashed; they love "teaching" and "learning" regardless of the content's validity; to question things is really a sin for them.

If I return to teleology, Carroll also writes:

Sure, maybe the underlying laws of nature are dysteleological, but surely there’s some useful sense in which macroscopic real-world systems can be usefully described using teleological language, even if it’s only approximate or limited in scope.

I don't think so. If there's some purpose in a particular history that a portion of the Universe follows, it's because "brains" or otherwise intelligent or programmed devices that are choosing the steps in order to achieve a goal, a final state. But it must have been clear to sharp thinkers for thousands of years – well before Galileo – that such a "purpose" cannot ever be a fundamental law of anything. A way to see that "purpose" is just wrong as a template for a physical law is to notice that our own dreams and wishes simply often disagree with the future reality. So wishes and the future reality are different things. That's why the future reality cannot be a direct consequence of anyone's wishes. Moreover, we know that our wishes are not fundamental; they are consequences of something else. We want to find water because we're thirsty and we may die after some time without liquids. Finally, we really roughly understand how the "planning for a purpose" works. We have the plan in our memory and produce one instruction after another what to do. We know that the ultimate materialization of the goal (if we're lucky) isn't a direct consequence of a mysterious fundamental law; it is a consequence of many steps in our thinking that we may disentangle.

(Here’s where I like to paraphrase Scott Derrickson: The universe has purposes. I know this because I am part of the universe, and I have purposes.)

No, it's just intelligent objects in the Universe and they have preferences. And it only makes sense to call them "purposes of their actions" if the goal is actually achieved which is in no way guaranteed.

It’s okay, I think, to say things like “predators tend to have sharp teeth because it helps them kill and eat prey,” even if we understand that those causes are merely local and contingent, not transcendent.

It's okay to say it but the human language may be misleading, as Aristotle failed to acknowledge. The problem is that the word "because" in that sentence isn't describing the "elementary cause" behind the existence of sharp teeth. The "explanation of the reason" only works within a framework of a theory – Darwin's theory – which envisions mechanisms that may build new or modified organs for new animals and that favors their proliferation if they are "useful".

But without such a mechanism, something's being "useful" doesn't imply something's existence. A flying car that may visit the whole Universe within seconds is "useful" but it doesn't exist.

The construction "A because B" may mean "B implies [or is the reason of] A" which is the proper logical and scientific way of using this construction; or it may mean "B is a possible purpose of A, something that makes or would make A useful". But these are two totally different relationships between A,B. In particular, the latter isn't a logical or scientific explanation of anything. I think that you may realize that this failure of Aristotle to distinguish between the two interpretations of the construction is correlated with his sloppy, grammar-like version of the mathematical logic.

If I return to the "purpose" of animals' behavior, we understand why it "seems" to exist. Animal species that have virtues improving their survival odds are very likely to proliferate and dominate and gradually replace the less viable ones. Being able to think "several moves ahead" is a virtue that generally improves the survival odds, and the more moves ahead an animal, human, or chess player may plan, the more teleological the behavior looks. But it's manifest – and it had to be manifest even long before the modern discoveries of the experimental science – that the ability to plan is an emergent feature of a sufficiently complex animal (one able to think).

Of course, Carroll does connect his musings with his delusions about the arrow of time:

In particular, the past had a low entropy: we can reconcile the directedness of macroscopic time evolution with the indifference of microscopic dynamics by positing some sort of Past Hypothesis (see also).

The existence of the past isn't a hypothesis; the existence of the past is a fact. More precisely, the past is the collection of all facts we may have at the present. Everything we know for sure is a property of the past, every question about future is at least slightly uncertain or unknowable.

We don't need any additional "past hypothesis" to prove the second law of thermodynamics within statistical physics. The increasing nature of entropy is an unavoidable consequence the statistical methods applied to general dynamical laws that evolve the future out of the past – whether the laws are deterministic or probabilistic. The asymmetry in the previous sentence, "the future evolves from the past but not vice versa", is absolutely essential for any probabilistic calculations. Whenever we deal with probabilities not equal to zero or one, with any incomplete knowledge, or with any predicates, the calculable probabilities simply depend on the logical arrow of time – which direction is the future and which direction is the past – because the past microstates are being averaged while the future states are being summed over. The thermodynamic arrow of time is derived from the logical one.

Sean Carroll not only defends his/their completely idiotic myth about the extra required prerequisites for the second law of thermodynamics – the "Past Hypothesis" – but to make his case stronger (in his eyes), he invented yet another term for the same thing. Archaeology (a possible opposite of "teleology") has already been taken so he picked aphormeology for some vague principle that is perhaps equivalent to the "Past Hypothesis" and perhaps it means some determinism (present determined by the past) or something completely different. I guess that Aristotle himself would be acting similarly – inventing lots of new Greek words for useless and vague concepts that bizarrely link several loosely connected or disconnected theoretical constructs and whose existence is mostly based on fundamental misunderstandings of how Nature works and what people have to do to realize how it works. This new terminology is created with the very purpose to encapsulate and shield all the misconceptions that have been thrown into the definition. If there's new trademark, it must be protected, right?

11 comments:

>> indefensible far-reaching gems like "spontaneous generation": organisms are created directly from some inorganic matter, from dust and mud,

This was still believed in the early 19th century...

They had no better explanation because they were depraved of crucial empirical information of the small and large scale structure of the world. Telescope and microscope just got developed in the 18th century!

"In 1837, de la Tour, a physicist, and Schwann, founders of cell theory, published their independent discovery of yeast in alcoholic fermentation. They used the microscope to examine foam left over from the process of brewing beer. Where Leeuwenhoek described "small spheroid globules", they observed yeast cells undergo cell division. Fermentation would not occur when sterile air or pure oxygen was introduced if yeast were not present. This suggested that airborne microorganisms, not spontaneous generation, was responsible"

Had they been invented 2000 years earlier, the world might have been very different...

> the calculable probabilities simply depend on the logical arrow of time – which direction is the future and which direction is the past – because the past microstates are being averaged while the future states are being summed over. The thermodynamic arrow of time is derived from the logical one.

It is true that the "logical" arrow of time implies the thermodynamic one, but also the thermodynamic arrow of time implies the logical one. If the thermodynamic arrow were reversed (entropy a decreasing function of t), you would have to sum over microstates for smaller t and average over states with larger t (and would call them "future" and "past" respectively).

The third law of thermodynamics implies that entropy was much lower in the past, but a very low entropy past also implies that entropy will increase.

The question "which of two equivalent statements is 'fundamental'"? should not be expected to have an unambiguous answer, but one may be preferred if it is implied by something more fundamental still.

You have argued that a cosmological explanation of the low entropy of the early universe is unnecessary, because it is implied by the third law of thermodynamics. But the implication works the other way as well.

I don't understand how the question could fail to have an answer. The entropy increase is a derived law - it is not even "strictly" true, it is just a statistical law, so it clearly can't be a starting point in deducing some law about summing or averaging - not to mention that there is no conceivable way how you could derive such a rule, is there?

Completely agree, but I would go even further and say the past is the collection of all classical observations that we can have record of. Entropy is simply a measure of irreversible observations and provides a means to synchronize with all other co-moving observers. Entropy is effectively how we measure time. That the universe started in a low entropy condition is simply no more confusing then to say the clock was near zero right after the big bang, which represents the beginning of our record of classical observations.

As co-moving observers it is non-sensical to ask if there was a larger entropy in the past, as it implies there is a larger set of classical observations that do not contribute to current observations. This violates our notions of classical mutual exclusiveness, we cannot simultaneously be in a state of high entropy and low entropy simultaneously under classical mutual exclusiveness. However, that is not completely the case in quantum mechanics. Unobserved systems can be in mutually exclusive states simultaneously and thus can be high or low entropy simultaneously. If we can assume everything in the co-moving plane is already observed in a low entropy state, we would probably see most observations to be compliant with that expectation.

Schrodinger's cat is a good analogy. The dead cat is arguably higher entropy then the alive cat. The alive cat is still working to release stored energy, so while environmental entropy might still be increasing, internally the cat is trying to keep entropy low. So the unobserved cat has mixed entropy. As long as the entropy of the box stays in sync with the observers, the entropy of the cat can be low or high.

Dhuu, reading Sean Carrolls original post would probably give me a headache, there might be too much fog spread and I always despised the invention of unneede new terminology/jargon in school in the context of some "soft" non science subjects where we had to interpret texts, pictures, artwork, etc ... Listening to a narrator at a so called "higher-level" radio station talking about the gravity of an authors text while driving with my car to work, made me LOL and almost miss the road ... ;-P

I think this text a nice and important reminder of what can happen (Dark Ages) if a too large crowd adheres blindly to the delusions of certain idol (Aristotle). Thinking too closely about it, it is rather shoking, and it can not be exluded that scientific and technical advancement will experiance a long hiatus or even a regress again, if we allow APODs and trolls to determin what smart people are allowed to do ... :-/

Ancient Greek philosophers had all kinds of theories, some closer to what we now know of physics and astronomy, and some not. But that is exactly my point, they had no way to decide which one was the correct one because they did not have the crucial access to observations on the large and small scale structure of the human world!